Three exponents
For one fan on one unchanged system, airflow is proportional to speed, static pressure to the square of speed and shaft power to the cube. Nothing else is needed. A blower at 800 RPM moving 1,000 CFM against 0.5 in wg at half a horsepower, taken to 960 RPM, moves 1,200 CFM against 0.72 in wg at 0.86 hp. Twenty percent more air, forty-four percent more pressure, seventy-three percent more power.
That last figure is the one that ends the conversation more often than not. A half-horsepower motor asked for 0.86 is being asked for something it may well not have, and the service factor is not a spare seventy-three percent. The exponents also mean the arithmetic works brutally in the other direction: a ten percent speed reduction gives up ten percent of the air and gets twenty-seven percent of the power back, which is the entire argument for variable speed.
Belt drives make speed adjustable, which is the point
A belt-drive blower runs at the motor speed times the motor sheave pitch diameter divided by the blower sheave pitch diameter. A 1,725 RPM motor with a 3.0 in sheave driving a 6.5 in blower sheave gives 796 RPM. To reach 960 with the same blower sheave, the motor sheave has to go to 3.62 in pitch diameter — which is why adjustable motor sheaves exist and why the setting on one matters as much as the part number.
Pitch diameter is the working number, not the outside diameter of the flange, and on an adjustable sheave it moves as the halves are threaded in or out. Measuring the outside and calling it the pitch diameter puts every figure here out by a few percent in a direction that is easy to miss.
When the laws do not apply
They describe a change of speed on an unchanged system. Open a damper, fit a lower-restriction filter, add a return, and the system curve itself has moved — the operating point does not slide along the old curve and none of the three relations hold. That is a different calculation entirely, and it usually needs the fan curve rather than the fan laws.
They also do not describe a variable-speed motor running a constant-airflow routine. Such a blower changes its speed specifically to keep airflow constant as the static pressure moves, which is the first fan law being deliberately violated by the control. Applying these three lines to one gives answers that look reasonable and are meaningless.
And the square law on pressure assumes the resistance behaves as a square law. Duct roughly does. A filter loading up does not, and worse, it changes while you are watching — so a before reading taken in March and an after reading taken in April are two different systems, not one change. Take them on the same day with the same filter.
What the page will not decide for you
Whether the motor can carry the new power, whether the blower can turn at the new speed, whether the belt and bearings are happy there, and whether the resulting airflow is right for the equipment — all of those live in the equipment data and none of them are arithmetic. The page gives the numbers the three laws produce and stops. It is also worth naming plainly that changing airflow across a furnace heat exchanger changes the temperature rise, and that anything altering the pressure a mechanical room sits at can change how a naturally drafted appliance vents. Those are matters for the equipment data and for whoever is qualified to work on it.
Questions people ask
What are the fan laws?
For one fan on one unchanged system: airflow is proportional to speed, static pressure to the square of speed, and shaft power to the cube. A blower going from 800 to 960 RPM gains twenty percent airflow, forty-four percent static pressure and seventy-three percent power. The relationship between those three percentages is fixed by the exponents and is the same for any fan.
Why does twenty percent more air cost seventy-three percent more power?
Because power carries the cube of the speed ratio, and 1.2 cubed is 1.728. It is the single most useful thing about the fan laws and the most frequently ignored: a motor sized for the original duty is not carrying a seventy-three percent increase, and the service factor is not a spare margin of that size. The same arithmetic run backwards is why slowing a blower ten percent returns twenty-seven percent of the power.
How do I work out blower RPM from the sheaves?
Motor speed times the motor sheave pitch diameter divided by the blower sheave pitch diameter. A 1,725 RPM motor with a 3.0 in motor sheave and a 6.5 in blower sheave gives 796 RPM. To land on a target speed with the blower sheave unchanged, multiply the target speed by the blower sheave diameter and divide by the motor speed. Use pitch diameters, not the outside of the flanges.
Do the fan laws work if I change the ductwork?
No. They describe a speed change on a system that stays put. Opening a damper, fitting a less restrictive filter or adding a return moves the system curve itself, so the operating point does not slide along the old one and none of the three relations hold. That case needs the fan curve for the machine rather than these three lines.
Do the fan laws apply to a variable-speed ECM blower?
Not when it is running a constant-airflow routine. Such a control changes speed on purpose to hold airflow steady as the static pressure moves, which is the first fan law being broken deliberately. The laws describe the fan itself; a constant-airflow control sits on top of the fan and overrides the relationship you would otherwise see between speed and flow.